First Order Linear Temporal Logic over Finite Time Structures

Cerrito, Serenella; Mayer, Marta Cialdea; Praud, S.

doi:10.1007/3-540-48242-3_5

Cited by 25 publications

(18 citation statements)

References 11 publications

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“…It is also known that to restrict the time domain is a technique that may be applied to obtain a decidable or efficient fragment of LTL [12]. Restricting the time domain implies not only some purely theoretical merits as mentioned above, but also some practical merits for describing temporal databases [7] and for implementing an efficient model checking algorithm, called bounded model checking [5]. Such practical merits are important due to the fact that there are problems in computer science and artificial intelligence where only a finite fragment of the time sequence is of interest [7].…”

Section: Why Do We Bound the Time Domain?mentioning

confidence: 97%

“…Such an idea was discussed, for instance, in [5,7,12]. By using and introducing a bounded time domain and the notion of bounded validity, bounded tableaux calculi (with temporal constraints) for propositional and first-order LTLs were studied by Cerrito, Mayer and Prand [7].…”

Section: Why Do We Bound the Time Domain?mentioning

confidence: 98%

“…Restricting the time domain implies not only some purely theoretical merits as mentioned above, but also some practical merits for describing temporal databases [7] and for implementing an efficient model checking algorithm, called bounded model checking [5]. Such practical merits are important due to the fact that there are problems in computer science and artificial intelligence where only a finite fragment of the time sequence is of interest [7]. We hope that IB[l] and PB[l] provide a good proof-theoretical basis for such practical applications as well as a good tool for automated reasoning with (bounded) linear-time formalisms.…”

Section: Why Do We Bound the Time Domain?mentioning

confidence: 99%

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Combining linear-time temporal logic with constructiveness and paraconsistency

Kamide

Wansing

2010

Journal of Applied Logic

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It is known that linear-time temporal logic (LTL), which is an extension of classical logic, is useful for expressing temporal reasoning as investigated in computer science. In this paper, two constructive and bounded versions of LTL, which are extensions of intuitionistic logic or Nelson's paraconsistent logic, are introduced as Gentzen-type sequent calculi. These logics, IB[l] and PB [l], are intended to provide a useful theoretical basis for representing not only temporal (linear-time), but also constructive, and paraconsistent (inconsistency-tolerant) reasoning. The time domain of the proposed logics is bounded by a fixed positive integer. Despite the restriction on the time domain, the logics can derive almost all the typical temporal axioms of LTL. As a merit of bounding time, faithful embeddings into intuitionistic logic and Nelson's paraconsistent logic are shown for IB [l] and PB[l], respectively. Completeness (with respect to Kripke semantics), cut-elimination, normalization (with respect to natural deduction), and decidability theorems for the newly defined logics are proved as the main results of this paper. Moreover, we present sound and complete display calculi for IB[l] and PB [l]. ] it has been emphasized that intuitionistic linear-time logic (ILTL) admits an elegant characterization of safety and liveness properties. The system ILTL, however, has been presented only in an algebraic setting. The present paper is the first semantical and proof-theoretical study of bounded constructive linear-time temporal logics containing either intuitionistic or strong negation.

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Section: Why Do We Bound the Time Domain?mentioning

confidence: 97%

Section: Why Do We Bound the Time Domain?mentioning

confidence: 98%

Section: Why Do We Bound the Time Domain?mentioning

confidence: 99%

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Combining linear-time temporal logic with constructiveness and paraconsistency

Kamide

Wansing

2010

Journal of Applied Logic

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“…A labeled tableau system for the LTL-fragment LTL[F] has been proposed by Schmitt and Goubault-Larrecq [29] (an attempt to extend it to full LTL is reported in [30]). Finally, a tableau method for PLTL over bounded models has been developed by Cerrito and Cialdea-Mayer [5] (in [6], Cerrito et al generalize the method to first-order PLTL). The satisfiability problem for LTL and PLTL is PSPACE-complete [31], while that for PLTL over bounded models of polynomial length and LTL[F] is NP-complete [5,31].…”

Section: Point-based Linear and Branching Temporal Logicsmentioning

confidence: 99%

A general tableau method for propositional interval temporal logics: Theory and implementation

Goranko

Montanari

Sala

et al. 2006

Journal of Applied Logic

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In this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's CDT logic interpreted over partial orders (BCDT + for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. ✩ This paper is an extended and revised version of [V. Goranko, A. Montanari, G. Sciavicco, A general tableau method for propositional interval temporal logics, in:

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“…To restrict the time domain in LTL is not a new idea. Such an idea was discussed, for example, in [3,4,6]. It is known that to restrict the time domain is a technique that may be applied to obtain a decidable or efficient fragment of LTL [6].…”

Section: Timementioning

confidence: 99%

Temporal non-commutative logic: Expressing time, resource, order and hierarchy

Kamide

2009

LLP

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A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and a resourceindexed non-commutative logic RN[l] is also shown. This theorem is intended to state that "time" is regarded as a "resource".

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First Order Linear Temporal Logic over Finite Time Structures

Cited by 25 publications

References 11 publications

Combining linear-time temporal logic with constructiveness and paraconsistency

Combining linear-time temporal logic with constructiveness and paraconsistency

A general tableau method for propositional interval temporal logics: Theory and implementation

Temporal non-commutative logic: Expressing time, resource, order and hierarchy

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